First of all, the time between the OPT end data and start of
your new program should not be more than 5 months. In this case you look fine.

You should be accepted for new study program either in the
same college or different college before the end of 60 days grace period
following OPT end date.

If you are going to new college, after getting acceptance
letter from your new school, you should apply for F1 release with your chosen
release date in your current college no later than end of 60 days grace period.
The release date must be no earlier than 5 months from new study start date.

Your current school then updates ur SEVIS record on the chosen release date and
your new school will then provide I-20 to you.

.

If you are planning to study on same college, you should first
be accepted for study  and apply for new
I-20 before the end of grace period.

You will be in legal status if above mentioned things went
timely.